Global existence and decay results of a viscoelastic wave equation with variable exponent and logarithmic nonlinearities

Abstract

In this work, we consider the following viscoelastic problem with variable exponents and logarithmic nonlinearities : We use the Faedo-Galerkin method to show that a weak solution exists locally, and we also demonstrate that a solution exists globally for the problem. Additionally, we explore general decay results for a wide range of relaxation functions and specific conditions for the variable exponent function. We conclude our results by presenting examples illustrating these results.